.. DO NOT EDIT.
.. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY.
.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE:
.. "auto_examples/gallery/plot_arc_density_model_example.py"
.. LINE NUMBERS ARE GIVEN BELOW.

.. only:: html

    .. note::
        :class: sphx-glr-download-link-note

        :ref:`Go to the end <sphx_glr_download_auto_examples_gallery_plot_arc_density_model_example.py>`
        to download the full example code.

.. rst-class:: sphx-glr-example-title

.. _sphx_glr_auto_examples_gallery_plot_arc_density_model_example.py:


Arc Density Constraint Model
=============================

This example demonstrates the ArcDensityConstraintModel which enforces energy density limits
in the plasma arc to prevent excessive thermal loading.

.. GENERATED FROM PYTHON SOURCE LINES 8-75



.. image-sg:: /auto_examples/gallery/images/sphx_glr_plot_arc_density_model_example_001.png
   :alt: Arc Energy Density vs Pulse Energy
   :srcset: /auto_examples/gallery/images/sphx_glr_plot_arc_density_model_example_001.png
   :class: sphx-glr-single-img


.. rst-class:: sphx-glr-script-out

 .. code-block:: none

    ==================================================
    Arc Density Constraint Model
    ==================================================
    Energy Density: 3.18e+05 J/m³
    Maximum Allowed: 1.00e+09 J/m³
    Margin: 1.00e+09 J/m³
    Constraint Satisfied: Yes
    ==================================================
    [OK] Energy density is within safe limits

    Generating plot: Energy Density vs Energy per Pulse...






|

.. code-block:: Python


    import matplotlib.pyplot as plt
    import numpy as np
    import openmdao.api as om

    from paroto.models.arc_density import ArcDensityConstraintModel

    # Create OpenMDAO problem with max energy density parameter
    prob = om.Problem()
    prob.model.add_subsystem(
        "density",
        ArcDensityConstraintModel(model_parameters={"max_energy_density": 1e9}),  # 1 GJ/m³
    )
    prob.setup()

    # Set parameters for typical operating conditions
    prob.set_val("density.energy_per_pulse", 10e-3)  # 10 mJ
    prob.set_val("density.thermal_diameter", 0.002)  # 2 mm arc diameter
    prob.set_val("density.arc_length", 0.01)  # 10 mm arc length

    # Run model
    prob.run_model()

    # Extract results
    rho_E = prob.get_val("density.energy_density")[0]
    margin = prob.get_val("density.density_margin")[0]
    satisfied = prob.get_val("density.density_constraint_satisfied")[0]

    print("=" * 50)
    print("Arc Density Constraint Model")
    print("=" * 50)
    print(f"Energy Density: {rho_E:.2e} J/m³")
    print("Maximum Allowed: 1.00e+09 J/m³")
    print(f"Margin: {margin:.2e} J/m³")
    print(f"Constraint Satisfied: {'Yes' if satisfied > 0.5 else 'No'}")
    print("=" * 50)

    if satisfied > 0.5:
        print("[OK] Energy density is within safe limits")
    else:
        print("[FAIL] Energy density exceeds maximum threshold")
        print("  Reduce energy per pulse or increase arc volume")

    # Plot energy density vs energy per pulse
    print("\nGenerating plot: Energy Density vs Energy per Pulse...")
    energy_range = np.linspace(1e-3, 50e-3, 50)  # 1 mJ to 50 mJ
    density_values = []
    max_density = 1e9  # J/m³

    for energy in energy_range:
        prob.set_val("density.energy_per_pulse", energy)
        prob.run_model()
        density_values.append(prob.get_val("density.energy_density")[0])

    plt.figure(figsize=(8, 5))
    plt.plot(
        energy_range * 1e3, np.array(density_values) / 1e9, "b-", linewidth=2, label="Energy Density"
    )
    plt.axhline(y=1.0, color="r", linestyle="--", linewidth=2, label="Max Allowed (1 GJ/m³)")
    plt.axvline(x=10, color="g", linestyle=":", alpha=0.7, label="Nominal (10 mJ)")
    plt.xlabel("Energy per Pulse (mJ)")
    plt.ylabel("Energy Density (GJ/m³)")
    plt.title("Arc Energy Density vs Pulse Energy")
    plt.grid(True, alpha=0.3)
    plt.legend()
    plt.tight_layout()
    plt.show()


.. rst-class:: sphx-glr-timing

   **Total running time of the script:** (0 minutes 0.159 seconds)


.. _sphx_glr_download_auto_examples_gallery_plot_arc_density_model_example.py:

.. only:: html

  .. container:: sphx-glr-footer sphx-glr-footer-example

    .. container:: sphx-glr-download sphx-glr-download-jupyter

      :download:`Download Jupyter notebook: plot_arc_density_model_example.ipynb <plot_arc_density_model_example.ipynb>`

    .. container:: sphx-glr-download sphx-glr-download-python

      :download:`Download Python source code: plot_arc_density_model_example.py <plot_arc_density_model_example.py>`

    .. container:: sphx-glr-download sphx-glr-download-zip

      :download:`Download zipped: plot_arc_density_model_example.zip <plot_arc_density_model_example.zip>`